Choose an operation
Matrix workspace
Result
A × B
19
22
43
50
How it was calculated
- 1.The inner dimensions match (2), so the result is 2 × 2.
- 2.First entry: 1 × 5 + 2 × 7 = 19.
- 3.Repeat the row-by-column dot product for every result entry.
Free step-by-step calculator
Free matrix calculator online
A matrix calculator performs operations on grids of numbers, including addition, multiplication, determinants, inverses, transposes, and row reduction. Enter matrices up to 5 × 5 to get an instant result with readable steps.
Matrix operation rules
Add or subtract
Use identical dimensions and combine entries in matching positions.
Multiply
The first matrix's column count must match the second matrix's row count.
Determinant and inverse
These operations require a square matrix. An inverse also requires a nonzero determinant.
RREF
Swap, scale, and combine rows until every pivot is the only nonzero value in its column.
Matrix calculator FAQ
What is a matrix calculator?
A matrix calculator performs operations on rectangular arrays of numbers, including addition, multiplication, determinants, inverses, transposes, and row reduction.
When can two matrices be multiplied?
Matrix A can multiply Matrix B when the number of columns in A equals the number of rows in B. The result has A's rows and B's columns.
Which matrices have an inverse?
Only square matrices with a nonzero determinant have an inverse. A matrix with determinant zero is singular and cannot be inverted.
What does RREF mean?
Reduced row echelon form uses row operations so every leading entry is 1 and is the only nonzero value in its column.
How large can the matrices be?
This browser calculator supports matrices from 1 × 1 through 5 × 5, which keeps step-by-step row operations readable.